Factor x^2+3x+4

Problem

x2+3*x+4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=3 and c=4

2. Calculate the discriminant to determine if the quadratic can be factored over the set of real numbers using the formula D=b2−4*a*c

3. Substitute the values into the discriminant formula: D=3−4*(1)*(4)=9−16=−7

4. Conclude that since the discriminant is negative (D<0, there are no real roots, and the expression is irreducible over the real numbers.

Final Answer

x2+3*x+4=irreducible over the real numbers

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